Answer:
$25.5 per hour.
Step-by-step explanation:
The function C(x) = 25.50x + 50 ........ (1) models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house.
Now, from the linear equation it is clear that the change in cost of cleaning from 3 hours and 9 hours are respectively {From equation (1)}
C(3) = 25.5 × 3 + 50 = $126.5 and
C(9) = 25.5 × 9 + 50 = $279.5
Therefore, the average rate of change of the function between 3 hours and 9 hours will be = [tex]\frac{\textrm {Change in price of cleaning}}{\textrm {Change in hours}}[/tex]
= [tex]\frac{279.5 - 126.5}{9 - 3}[/tex]
= $25.5 per hour. (Answer)
A farmer in China discovers a mammal hide that contains 37% of its original amount of C-14. Find the age of the mammal hide to the nearest year.
Answer: 54678 years
Step-by-step explanation:
This can be solved by the following equation:
[tex]N_{t}=N_{o}e^{-\lambda t}[/tex] (1)
Where:
[tex]N_{t}=54\%=0.54[/tex] is the quantity of atoms of carbon-14 left after time [tex]t[/tex]
[tex]N_{o}=1[/tex] is the initial quantity of atoms of C-14 in the mammal hide
[tex]\lambda[/tex] is the rate constant for carbon-14 radioactive decay
[tex]t[/tex] is the time elapsed
On the other hand, [tex]\lambda[/tex] has a relation with the half life [tex]h[/tex] of the C-14, which is [tex]5730 years[/tex]:
[tex]\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}[/tex] (2)
Substituting (2) in (1):
[tex]0.54=1e^{-(0.000121 years^{-1}) t}[/tex] (3)
Applying natural logarithm on both sides of the equation:
[tex]ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})[/tex] (4)
[tex]-0.616=-(0.000121 years^{-1}) t[/tex] (5)
Isolating [tex]t[/tex]:
[tex]t=\frac{-0.616}{-0.000121 years^{-1}}[/tex] (6)
[tex]t=54677.68 years \approx 54678 years[/tex] (7) This is the age of the mammal hide
The age of the mammal hide to the nearest year is approximately 11,239 years.
To find the age of the mammal hide with 37% of its original amount of C-14 remaining, we can use the decay formula for a substance undergoing exponential decay, which is described by the equation N(t) = N0(1/2)t/T, where N(t) is the remaining amount of substance, N0 is the original amount of substance, t is the time that has elapsed, and T is the half-life of the substance.
In this case, the half-life of C-14 is 5,730 years. Since we know the remaining amount of C-14 is 37% of the original amount, we can set up the equation 0.37 = (1/2)t/5730. To solve for t, we take the natural logarithm of both sides:
ln(0.37) = ln((1/2)t/5730)
ln(0.37) = (t/5730) * ln(1/2)
t = (ln(0.37)/ln(1/2)) * 5730
When we compute the value for t, we get the age of the mammal hide. By performing this calculation, we find that t is approximately 11,239 years. This is the estimated age of the mammal hide to the nearest year.
Select the correct answer.
A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2).
What is a reasonable time for it to take the baseball to land on the ground?
A.
7 seconds
B.
2 seconds
C.
9 seconds
D.
5 seconds
Answer:The reasonable time for the base ball to land on the ground is 5 seconds
Step-by-step explanation:
To get the time we will differentiate
h(t) = -16t2 + 80t + 224, w.r.t t
dh(t)/dt= 0
-32t +80=0
32t=80
t=80/32
t= 2.5 seconds This is the time the base ball has been in the air
The reasonable time for it to take the baseball to land on the ground is T= 2×t
T= 2×2.5
T=5 seconds
is 2×3×4the prime factorization of 24 Explain you reasoning
Answer:
see the prime factors
Step-by-step explanation:
24= 6*4=3*2*2*2
=2*3*4
Answer:
No
Step-by-step explanation:
First off, the number 4 is not a prime number and the prime factorization of a number has to consist of all prime numbers. 2*3*4 does result in 24 but 4 is not prime because a prime number is a whole number with exactly two factors, itself and 1. 4 has more than two factors; the factors of 4 are 1, 2, and 4 so 4 isn't prime.
2*2*2*3 is the prime factorization of 24 because when you break down 24 into prime numbers, the results are 2*2*2*3.
24=2*12(here, we broke the number 24 into two factors 2 and 12. it doesn't matter which factors you break the number into because you still get the same result.)
2*12=2*2*6(we broke the number 12 into 2*6 because 12 isn't prime. we have to break each number into prime numbers.)
2*2*6=2*2*2*3(finally, we broke down 6 because it is the only number left that is not prime. 2*3=6 and 2 and 3 are prime so we break down 6 into 2*3)
Now you have the prime factorization of 24!
24=2*2*2*3
Dere me pest answer for the question.
14. 20 is what percent of 50?
O A. 30%
OB. 10%
O C.40%
D.250%
Mark for review (Will be highlighted on the review page)
Answer:
C : 40%
Step-by-step explanation:
20 ÷ 50 = 0.40 also to solve just divide the smaller number from the greater number in order to be able to get the correct percentage.
Answer:
Step-by-step explanation
is / of = % / 100.....proportion formula
20 is what percent of 50...
20 / 50 = x / 100
cross multiply
50x = 2000
x = 2000/50
x = 40.......so 20 is 40% of 50
What is the equation of the following graph in vertex form?
y = (x − 3)^2 − 1
y = (x + 3)^2 − 1
y = (x − 4)^2 − 2
y = (x − 4)^2 + 8
============================================
How I got that answer:
The vertex is the lowest point of parabolas that open upward.
(h,k) = vertex
(h,k) = (-3,-1)
h = -3
k = -1
For each of the answer choices, a = 1.
The general template of a quadratic in vertex form is
y = a(x-h)^2 + k
Plug a = 1, h = -3, k = -1 into that equation. Simplify.
y = a(x-h)^2 + k
y = 1(x-(-3))^2 + (-1)
y = (x+3)^2 - 1
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola. The provided equations have vertices at different points. You must match the vertex of your graph with the correct equation.
Explanation:In order to find the equation of the graph in vertex form, we need to locate the vertex on the graph. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.
Considering the options provided:
y = (x − 3)² − 1: The vertex is at (3, -1)y = (x + 3)² − 1: The vertex is at (-3, -1)y = (x − 4)² − 2: The vertex is at (4, -2)y = (x − 4)² + 8: The vertex is at (4, 8)However, without a graph or specific vertex provided, we won't be able to define the equation of the graph precisely in vertex form. You need to match the vertex of your graph to one of the above options.
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A bicycle store costs $3850 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $155. How many bicycles must the store sell each month to break even?
155-45=110
3850÷110=385 bicycles
Answer:
35
Step-by-step explanation:
3850/(155-45)
3850/110
35
Hope this helps and please follow me ;)
Factorise 1 - 25 (a+b)^2
Answer:
Step-by-step explanation:
1 - 25 (a+b)^2 = 1 - 5² (a+b)²
= 1 - (5*[a + b) ]² { [tex]a^{m} *a^{n} = a^{m+n}[/tex] }
= 1 - (5a +5b)²
= (1 + 5a +5b) (1 - [5a + 5b]) { a² - b² = (a + b)(a - b) }
=(1 + 5a +5b) (1- 5a - 5b)
Find cos A if a=5, c=13
Answer:
You're not giving enough details about the figure
Select the equation of the line that passes through the point (–2, –1) and has slope 5 in point-slope form. a (y + 1) = 5(x + 2) b (x + 2) = 5(y – 1) c (y – 1) = 5(x – 2) d (x – 2) = 5(y + 1)
Answer:
y+1=5(x+2)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=5(x-(-2))
y+1=5(x+2)
An experimental vehicle is able to travel 3/8 mile on 1/16 gallon of water. What is the rate at which the vehicle can travel, in miles per gallon of water?
The rate at which the vehicle can travel is 6 miles per gallon
Solution:
Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water
To find: Rate at which the vehicle can travel, in miles per gallon of water
distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]
gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]
Miles per gallon is given as:
[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]
Substituting the given value we get,
[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]
So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon
The coordinates of the vertices of quadrilateral ABCD are A(-5, 1), B(-2,5), C(5, 3),
and D(2, -1)
Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is
the slope of BC is
, the slope of CD is
and the
slope of AD is!
Quadrilateral ABCD is
because
Answer:
The slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel.
Step-by-step explanation:
The quadrilateral ABCD has vertices A(-5,1), B(-2,5), C(5,3) and D(2,-1).
Now, slope of line AB = [tex]\frac{5 - 1}{- 2 - ( - 5)} = \frac{4}{3}[/tex]
Slope of line BC = [tex]\frac{3 - 5}{5 - (- 2)} = - \frac{2}{7}[/tex]
Slope of line CD = [tex]\frac{- 1 - 3}{2 - 5} = \frac{4}{3}[/tex]
And slope of DA = [tex]\frac{1 - ( - 1)}{- 5 - 2} = -\frac{2}{7}[/tex]
Therefore, the slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel. (Answer)
Answer:
The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3, and the slope of AD is -2/7. Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.
Step-by-step explanation:
A bicycle store costs $3600 per month to operate. The store pays an average of $75 per bike. The average selling price of each bicycle is $115. How many bicycles must the store sell each month to break
even?
The store must sell bicycles each month to break even.
(Type a whole number.)
I am not sure if i understand that 3600 is the cost of all the bikes they have bought in total, but they would have to sell 31 bikes to break even.
Linear or Non - Linear
Answer:
linear
Step-by-step explanation:
This graph is linear
Anyone for geometry #’s 5 & 6
Answer:
5. m < 1 = 72 degrees.
6. m < 1 = 80 degrees.
Step-by-step explanation:
5. < 1 = 72 degrees.
If we draw a line through the point of < 1, We see that We have have 2 angles of 40 and 32 ( alternate angles).
6. By the same reasoning m < 1 = 60 + 20
= 80 degrees.
Quadrilateral ABCD is translated up and to the right, and then
rotated about point Q. Which congruency statement is
correct?
ABCD = WXYZ
ABCD = ZYXW
ABCD WZYX
ABCD = ZWXY
When a triangle is translated, the resulting triangle will be congruent to the original triangle.
The congruency statement is ABCD = ZYXW
From the complete question, corresponding points are:
Point A and point ZPoint B and point YPoint C and point XPoint D and point WThis means that:
Points A and Z are correspondingPoints B and Y are correspondingPoints C and X are correspondingPoints D and W are correspondingHence, the congruency statement is ABCD = ZYXW
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The job paid $25 for every 2 hours of work. Write an equation that represents how much the job pays, y, for x hours of work.
We know that we can use y for "how much the job pays" and x for "hours of work."
Let's find how much the job pays in 1 hour by dividing.
25 / 2 = $12.5 per hour
We can mulitply x to 12.5 because this shows how much he earned.
An equation will look like 12.5x = y
Best of Luck!
The job pays $12.50 per hour. The equation to represent the pay, y, for x hours of work is 'y = 12.5x', which depicts direct proportionality.
Explanation:To solve this question, you must first understand that the job pays $25 for every 2 hours worked. Therefore, to find out how much the job pays for x hours of work, you'd simply multiply the rate per hour ($12.50, since $25 divided by 2 is $12.50) by x hours.
The equation that represents how much the job pays, y, for x hours of work is: y = 12.5x.
Here, 'y' denotes the total payment received and 'x' is the number of hours worked. This format is commonly used in equations representing direct proportionality, where one variable (in this case, pay) changes directly as the other (hours worked).
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Find the length of line segment GF
right triangle E F G; angle G is a right angle; side EF has a length of 9 point 4; side EG has a length of 6 point 8
Final answer:
To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. Plug in the given values of the lengths of the legs EF and EG, and solve the equation to find the length of GF.
Explanation:
To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is line segment GF. Let's label the length of EF as x, and the length of EG as y.
Using the Pythagorean theorem, we can set up the following equation: x^2 + y^2 = GF^2.
Plugging in the given values, x = 9.4 and y = 6.8, we get: 9.4^2 + 6.8^2 = GF^2. Solving this equation will give us the length of line segment GF.
The combined height of one fir tree and one pine tree is 21 meters. The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree. How tall are the types of trees?
The fir trees are 9 meters tall and the pine trees are 12 meters tall
Solution:
Let f be the height of one fir tree
Let p be the height of one pine tree
Given that combined height of one fir tree and one pine tree is 21 meters
So we get,
height of one fir tree + height of one pine tree = 21
f + p = 21 ----- eqn 1
Also given that height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree
height of 4 fir trees stacked on top of each other = 24 + height of one pine tree
4f = 24 + p ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "f and "p"
From eqn 1,
f = 21 - p ----- eqn 3
Substitute eqn 3 in eqn 2
4(21 - p) = 24 + p
84 - 4p = 24 + p
-4p - p = 24 - 84
-5p = - 60
p = 12Substitute p = 12 in eqn 3
f = 21 - 12 = 9
f = 9Summarizing the results:
height of one fir tree = 9 meters
height of one pine tree = 12 meters
Write an equation of the line passing through point P that is perpendicular to the given line. P(4,−3), y=−x−5
Answer:
all work is shown and pictured
if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle
Answer:
The measure of the third angle is a 90 degrees
Step-by-step explanation:
Let
A and B ----> two complementary angles in a triangle
C ---> the measure of the third angle in a triangle
we know that
If two angles are complementary, then their sum is equal to 90 degrees
so
[tex]A+B=90^o[/tex] ---> equation A
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]A+B+C=180^o[/tex] ----> equation B
substitute equation A in equation B
[tex](90^o)+C=180^o[/tex]
solve for C
subtract 90 degrees both sides
[tex]C=180^o-90^o[/tex]
[tex]C=90^o[/tex]
therefore
we have a right triangle
Which equation represents the line that passes through the points (-3,7) and (3,3)
Answer:
The equation of the line is 2 x +3 y = 15.
Step-by-step explanation:
Here the given points are ( -3, 7) & ( 3, 3) -
Equation of a line whose points are given such that
[tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-
y - [tex]y_{1}[/tex] = [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex] ( x - [tex]x_{1}[/tex] )
i.e. y - 7= [tex]\frac{3 - 7}{3 - (-3)}[/tex] ( x- (-3))
y - 7 = [tex]\frac{-4}{3 + 3}[/tex] ( x + 3 )
y - 7= [tex]- \frac{2}{3}[/tex] ( x + 3 )
3 ( y - 7) = - 2 ( x + 3)
3 y -21 = -2 x - 6
2 x + 3 y = 21 - 6
2 x + 3 y = 15
Hence the equation of the required line whose passes trough the points ( - 3, 7) & ( 3, 3) is 2 x + 3 y = 15.
Ms.Graves gave her class 18 minutes to read. Carrie read 6 1/2 pages in that time. At what rate, in pages per hour, did Carrie read?
Answer:
Carrie read at a rate of 21 2/3 pages per hour
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Time Ms. Graves gave her class to read = 18 minutes
Number of pages Carrie read in 18 minutes = 6 1/2 pages
2. At what rate, in pages per hour, did Carrie read?
Rate = Number of pages/Time given
For getting the exact rate per hour, we should use the Rule of Three Simple, this way:
Number of pages in 60 minutes * 18 = 6 1/2 * 60
Number of pages in 60 minutes = (6.5 * 60)/18
Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3
Carrie read at a rate of 21 2/3 pages per hour
Corresponding sides of similar triangles are
A opposite
B proportional
C equals
find the area of a trapezoid with base 1 side = 10 base 2 side = 16 and 3
Answer:
Area of Trapezoid is 39 unit²
Step-by-step explanation:
Given as :
For A Trapezoid
The measure of base side 1 = [tex]b_1[/tex] = 10 unit
The measure of base side 2 = [tex]b_2[/tex] = 16 unit
The height of the Trapezoid = h = 3 unit
Let The Area of Trapezoid = A square unit
Now, From Formula
Area of Trapezoid = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height
I.e A = [tex]\dfrac{1}{2}[/tex] × ([tex]b_1[/tex] + [tex]b_2[/tex]) × h
Or, A = [tex]\dfrac{1}{2}[/tex] × (10 unit + 16 unit) × 3 unit
Or, A = [tex]\dfrac{1}{2}[/tex] × (26 unit) × 3 unit
Or, A = [tex]\dfrac{1}{2}[/tex] × 78 unit²
Or, A = [tex]\dfrac{78}{2}[/tex] unit²
I.e A = 39 unit²
So, The Area of Trapezoid = A = 39 unit²
Hence, The Area of Trapezoid is 39 unit² . Answer
An Atlas moth has a wingspan of 11 inches. What is the wingspan of 26 Atlas moths?
Answer:
The wingspan of 26 atlas moths are 286 inches.
Step-by-step explanation:
Given:
An Atlas moth has a wingspan of 11 inches.
Now, to find the wingspan of 26 atlas moths.
So, we use unitary method:
As given an atlas wingspan has 11 inches.
Then for wingspan of 26 atlas we multiply it by 11 inches:
⇒ [tex]26\times 11\ inches[/tex]
[tex]=286\ inches.[/tex]
Therefore, the wingspan of 26 atlas moths are 286 inches.
Final answer:
To find the total wingspan of 26 Atlas moths, multiply the wingspan of one moth, 11 inches, by 26, resulting in a total of 286 inches.
Explanation:
The question involves simple multiplication to determine the total wingspan of 26 Atlas moths. If one Atlas moth has a wingspan of 11 inches, then the wingspan of 26 Atlas moths can be found by multiplying 11 inches by 26.
Step-by-step calculation:
Determine the wingspan of one Atlas moth, which is already given as 11 inches.
Multiply the wingspan of one moth by the total number of moths: 11 inches * 26 = 286 inches.
Therefore, the total wingspan of 26 Atlas moths is 286 inches.
What is 3 to the power of three halves equal to?
Answer: The answer is 5.2 (rounded to the nearest tenth)
Actual Answer: 5.19615242
Hope this helps!
Answer:
its the square root of 27 to the power of 2
Step-by-step explanation: hope this helps
Idk how to do this. Someone please help. This is a Geometry Honors class
Answer:
4.0
Step-by-step explanation:
AB / AC = AE / AD
1 / 4.5 = AE / 18
4.5 AE = 18
AE = 4.0
Since BE and CD are parallel, triangles ABE and ACD are similar, meaning their side lengths are proportional.
AC = AB + BC = 1 + 3.5 = 4.5
The proportion of AB to AC (corresponding sides of two similar triangles) is 1 / 4.5
Let x be the variable that represents the unknown length of AE
The proportion of AE to AD (another set of corresponding sides of two similar triangles) is x / 18
Since the triangles are similar, these two proportions must be equal.
1 / 4.5 = x / 18
Cross multiply
4.5x = 18
Divide both side by 4.5
x = 4
The length of AE is 4, no need to round since the answer is already a whole number.
Let me know if you need any clarifications, thanks!
3 x 1/3 divided by 2 x 3 to the second power
Answer:
1/36
Step-by-step explanation:
3(1/3)=3/3=1
2*3=6
(1/6)^2=(1/6)(1/6)=1/36
given f(x)=2x^2+3x-5 for what values of x is f(x) positive
Answer:
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
Step-by-step explanation:
we have
[tex]f(x)=2x^{2}+3x-5[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
The coordinates of the vertex is the point (h,k)
step 1
Find the vertex of the quadratic function
Factor the leading coefficient 2
[tex]f(x)=2(x^{2}+\frac{3}{2}x)-5[/tex]
Complete the square
[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}[/tex]
[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}[/tex]
Rewrite as perfect squares
[tex]f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}[/tex]
The vertex is the point (-\frac{3}{4},-\frac{49}{8})
step 2
Find the x-intercepts (values of x when the value of f(x) is equal to zero)
For f(x)=0
[tex]2(x+\frac{3}{4})^{2}-\frac{49}{8}=0[/tex]
[tex]2(x+\frac{3}{4})^{2}=\frac{49}{8}[/tex]
[tex](x+\frac{3}{4})^{2}=\frac{49}{16}[/tex]
take the square root both sides
[tex]x+\frac{3}{4}=\pm\frac{7}{4}[/tex]
[tex]x=-\frac{3}{4}\pm\frac{7}{4}[/tex]
[tex]x_1=-\frac{3}{4}+\frac{7}{4}=1[/tex]
[tex]x_2=-\frac{3}{4}-\frac{7}{4}=-2.5[/tex]
therefore
The function f(x) is negative in the interval (-2.5,1)
The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)
see the attached figure to better understand the problem
pls helpppppp!! before 12!
The answer is 25.12 exactly